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National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Stochastic mortality models within the quantification of selected actuarial risks
 Šešulka, Marek ; Hendrych, Radek (advisor) ; Mazurová, Lucie (referee)
The thesis focuses on the stochastic mortality models in the context of actuarial risks. In the theoretical part, the thesis defines five mortality models with approaches to prediction. After that, it follows the description of selected actuarial risks in the context of mortality. Hedging of longevity risk is obtained through a financial instrument called a longevity bond. Pricing of that bond is delivered via the Wang transformation approach. In the empirical part of the thesis, there are carried out estimates, interpretations, and comments for models based on the Czech mortality data. Later, prediction tests are executed for an individual model, both sex and two chosen ages. The last part of the empiric section deals with the data driven pricing of longevity bond and the price of risk.
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Exact penalization in optimization
 Šešulka, Marek ; Branda, Martin (advisor) ; Kopa, Miloš (referee)
This thesis deals with one of the possible different approaches to solving nonlinear optimization problems by convertion to finding non-bounded extrema of function, where constrains are transfered to objective function via penalty function. We will introduce exterior penalty function method and appropriate algorithm for solving this type for problems. The thesis also deals with exact penalty functions, which do not requires limit approximation of the penalty pa- rameter to infinity. Then we deal with integer binary nonlinear progamming, where several suitable penalty functions are presented to solve this type of pro- blem. In the numerical part, the thesis deals with the minimization of risk at the specifed minimum expected return on the sparse portfolio. We observe the effect of changing the penalty parameter on the results of ten different minimization problems calculating risk of sparsity portfolios. 1
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2 Šešulka, Michael
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